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NEET • PHYSICS • MOTION IN PLANE

Motion in plane practice · Medium

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Showing 1-30 of 176 questions
1 Medium
1 of 176
Understanding +4 | -1
The magnitudes of the two vectors a⃗ and b⃗\mathrm{\vec a}\,and\,\mathrm{\vec b} are a and b respectively. The vector product of a⃗ and b⃗\mathrm{\vec a}\,and\,\mathrm{\vec b} cannot be
View answer and explanation
Correct option: D
greater than ab
The vector product of a⃗ and b⃗\mathrm{\vec a}\,and\,\mathrm{\vec b} cannot be greater than ab because the magnitude of the cross product is absin⁡θab \sin \theta, and the maximum value of sin⁡θ\sin \theta is 1.
2 Medium
2 of 176
Analyzing +4 | -1
If P→  .  Q→=0 and P→  ×  Q→=0\overrightarrow P \,\,.\,\,\overrightarrow Q = 0\,and\,\overrightarrow P \,\, \times \,\,\overrightarrow Q = 0, then the angle between Q→ and R→\overrightarrow Q \,and\,\overrightarrow R is
View answer and explanation
Correct option: B
900{90^0}
Option B (900{90^0}) is correct because if P→.Q→=0\overrightarrow P \\. \overrightarrow Q = 0 and P→,×,Q→=0\overrightarrow P \\, \times \\, \overrightarrow Q = 0, then both vectors must be null vectors, which means any vector \overrightarrow R is perpendicular to \overrightarrow Q.
3 Medium
3 of 176
Understanding +4 | -1
What happens, when we multiply a vector by -2 ?
View answer and explanation
Correct option: B
Direction reverses and magnitude is doubled
Option B (Direction reverses and magnitude is doubled) is correct because multiplying a vector by a negative scalar reverses its direction, and multiplying by the absolute value of the scalar (2) doubles its magnitude.
4 Medium
4 of 176
Analyzing +4 | -1
Which of the following is not true? If A⃗=3i^+4j^\vec{A}=3 \hat{i}+4 \hat{j} and B⃗=6i^+8j^\vec{B}=6 \hat{i}+8 \hat{j} where AA and BB are the magnitudes of A→\overrightarrow{\mathrm{A}} and B→\overrightarrow{\mathrm{B}}
View answer and explanation
Correct option: C
A⃗⋅B⃗=48\vec{A} \cdot \vec{B}=48
Option C (A⃗⋅B⃗=48\vec{A} \cdot \vec{B}=48) is not true because the dot product of A⃗\vec{A} and B⃗\vec{B} is actually 3(6) + 4(8) = 18 + 32 = 50, not 48.
5 Medium
5 of 176
Analyzing +4 | -1
The wind appears to blow from the north to a man moving in the north-east direction. When he doubles his velocity the wind appears to move in the direction cot⁡−1(2){\cot ^{ - 1}}\left( 2 \right) east of north. The actual direction of the wind is
View answer and explanation
Correct option: D
v2\frac{v}{{\sqrt 2 }} towards east
Option D (v2\frac{v}{{\sqrt 2 }} towards east) is correct because it represents the actual wind direction, calculated using relative velocity concepts and vector addition.
6 Medium
6 of 176
Application +4 | -1
The resultant of two forces, each P, acting at an angle θ\theta is
View answer and explanation
Correct option: B
2P Cosθ2\frac{\mathrm{\theta }}{2}
Option B (2P Cosθ2\frac{\mathrm{\theta }}{2}) is correct because the resultant of two forces of equal magnitude P acting at an angle θ\theta is given by R=P2+P2+2P2cos⁡θ=2P2(1+cos⁡θ)=2P2(2cos⁡2θ2)=2Pcos⁡θ2R = \sqrt{P^2 + P^2 + 2P^2 \cos \theta} = \sqrt{2P^2(1 + \cos \theta)} = \sqrt{2P^2(2 \cos^2 \frac{\theta}{2})} = 2P \cos \frac{\theta}{2}.
7 Medium
7 of 176
Understanding +4 | -1
Which of the following conditions are sufficient and essential for a quantity to be a vector?
View answer and explanation
Correct option: C
Magnitude, direction, and addition, subtraction multiplication and division by vector laws
Option C is correct because a vector requires magnitude, direction, and adherence to vector addition, subtraction, multiplication, and division laws.
8 Medium
8 of 176
Understanding +4 | -1
The shape of trajectory of the motion of an object is determined by
View answer and explanation
Correct option: D
All of these
Option D is correct because the trajectory's shape depends on the object's acceleration, initial position, and initial velocity.
9 Medium
9 of 176
Understanding +4 | -1
Statement-I: If θ\theta be the angle between a⃗\vec{a} and b→\overrightarrow{\mathrm{b}}, then tan⁡θ=∣a⃗×b⃗∣a⃗⋅b⃗\tan \theta=\frac{|\vec{a} \times \vec{b}|}{\vec{a} \cdot \vec{b}}
Statement-II: a⃗×b⃗\vec{a} \times \vec{b} is perpendicular to a⃗.b⃗\vec{a} . \vec{b}
View answer and explanation
Correct option: B
Statement-I is true and statement-II is false
Statement-I is true because the tangent of the angle between two vectors is indeed the ratio of the magnitude of their cross product to their dot product. Statement-II is false because the cross product and dot product result in a vector and a scalar, respectively, so they cannot be perpendicular.
10 Medium
10 of 176
Application +4 | -1
A body is under the action of two mutually perpendicular forces of 3 N and 4 N. The resultant force acting on the body is
View answer and explanation
Correct option: C
5 N
Option C (5 N) is correct because the resultant of two perpendicular forces is found using the Pythagorean theorem.
11 Medium
11 of 176
Understanding +4 | -1
A bullet is fired with a velocity u making an angle of 600{60^0} with the horizontal plane. The horizontal component of the velocity of the bullet when it reaches the maximum height is
View answer and explanation
Correct option: D
u/2
Option D (u/2) is correct because the horizontal component of velocity remains constant throughout the projectile's motion and is equal to ucos⁡(60∘)=u/2u \cos(60^\circ) = u/2.
12 Medium
12 of 176
Analyzing +4 | -1
Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Two identical balls A and B thrown with same velocity ’u’ at two different angles with horizontal attained the same range R. If A and B reached the maximum height h1{h_1} and h2{h_2} respectively, then R=4h1h2R = 4\sqrt {{h_1}{h_2}}
Reason R: Product of said heights.
h1h2=(u2sin⁡2θ2g).(u2cos⁡2θ2g){h_1}{h_2} = \left( {\frac{{{u^2}{{\sin }^2}\theta }}{{2g}}} \right).\left( {\frac{{{u^2}{{\cos }^2}\theta }}{{2g}}} \right) Choose the correct answer:
View answer and explanation
Correct option: A
Both A and R are true and R is the correct explanation of A
Option A is correct because both the assertion and reason are true, and the reason correctly explains the assertion.
13 Medium
13 of 176
Understanding +4 | -1
Two non-zero vectors A→ and B→\overrightarrow A \,and\,\overrightarrow B are essentially perpendicular if
View answer and explanation
Correct option: A
A→ . B→=0\overrightarrow A \,.\,\overrightarrow B = 0
Option A is correct because two vectors are perpendicular if their dot product is zero.
14 Medium
14 of 176
Analyzing +4 | -1
In a tetrahedron OABCO A B C, the edges are of lengths, ∣OA∣=∣BC∣=a,∣OB∣=∣AC∣=b,∣OC∣=∣AB∣=c|O A|=|B C|=a,|O B|=|A C|=b,|O C|=|A B|=c. Let G1G_1 and C2C_2 be the centroids of the triangle ABCA B C and AOCA O C such that OG1⊥BG2O G_1 \perp B G_2, then the value of a2+c2b2\frac{a^2+c^2}{b^2} is
View answer and explanation
Correct option: B
3
Option A (3) is correct because the condition OG1⊥BG2OG_1 \perp BG_2 leads to the equation a2+c2=3b2a^2 + c^2 = 3b^2, thus a2+c2b2=3\frac{a^2+c^2}{b^2} = 3.
15 Medium
15 of 176
Analyzing +4 | -1
Given that C⃗=A⃗+B⃗\vec{C}=\vec{A}+\vec{B} and C⃗\vec{C} makes an angle α\alpha with A⃗\vec{A} and β\beta with B⃗\vec{B}. Which of the following options is correct?
View answer and explanation
Correct option: C
α<β\alpha < \beta, if A>BA > B
Option C (α<β\alpha < \beta, if A>BA > B) is correct because the angle a vector makes with another vector is inversely proportional to its magnitude when they are added.

Explore Other Chapters in PHYSICS

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UNITS & MEASUREMENTS 392 MCQs WORK-ENERGY-POWER 355 MCQs MECHANICAL PROPERTIES OF FLUIDS 317 MCQs MAGNETIC EFFECT OF CURRENT 282 MCQs THERMAL PROPERTIES OF MATTER 269 MCQs GRAVITATION 258 MCQs
16 Medium
16 of 176
Remembering +4 | -1
A vector multiplied by the number 0, results into
View answer and explanation
Correct option: C
0\boldsymbol{0}
Option C (0\boldsymbol{0}) is correct because multiplying any vector by the scalar 0 results in the zero vector.
17 Medium
17 of 176
Analyzing +4 | -1
It is found that ∣A+B∣=∣A∣,\left| {A + B} \right| = \left| A \right|, this necessarily implies
View answer and explanation
Correct option: A
B=0B = 0
Option A (B=0B = 0) is correct because if the magnitude of A+B equals the magnitude of A, it implies B must be a zero vector.
18 Medium
18 of 176
Application +4 | -1
If F→=i^+2j^−3k^\overrightarrow F = \widehat i + 2\widehat j - 3\widehat k and r→=2i^−j^+k^\overrightarrow r = 2\widehat i - \widehat j + \widehat k. Find r→×F→\overrightarrow r \times \overrightarrow F
View answer and explanation
Correct option: B
i^+7j^+5k^\widehat i + 7\widehat j + 5\widehat k
Option B (i^+7j^+5k^\widehat i + 7\widehat j + 5\widehat k) is correct because it is the result of the cross product of the two given vectors.
19 Medium
19 of 176
Understanding +4 | -1
Statement-I: The scalar product of a force F⃗\vec{F} and displacement r⃗\vec{r} is equal to the work done.
Statement-II: Work done is not a scalar.
View answer and explanation
Correct option: B
Statement-I is true and statement-II is false
Option B (Statement-I is true and statement-II is false) is correct because work done is a scalar quantity, calculated as the dot product of force and displacement.
20 Medium
20 of 176
Understanding +4 | -1
The relation between the time of flight of a projectile Tf{T_f} and the time to reach the maximum height tm{t_m} is
View answer and explanation
Correct option: A
Tf=2tm{T_f} = 2{t_m}
Option A (Tf=2tm{T_f} = 2{t_m}) is correct because the time of flight is twice the time to reach the maximum height in projectile motion.
21 Medium
21 of 176
Understanding +4 | -1
Statement-I: Minimum number of non-equal vectors in a plane required to give zero resultant is three.
Statement-II: If a⃗+b⃗+c⃗=0\vec{a}+\vec{b}+\vec{c}=0, then they must lie in one plane
View answer and explanation
Correct option: A
Statement-I is true and statement-II is true
Option A (Statement-I is true and statement-II is true) is correct because at least three non-equal vectors in a plane are needed for a zero resultant, and if the sum of three vectors is zero, they must lie in one plane.
22 Medium
22 of 176
Understanding +4 | -1
Three vectors A→,  B→,  C→\overrightarrow A ,\,\,\overrightarrow B ,\,\,\overrightarrow C satisfy the relation A→.B→ =0\overrightarrow A .\overrightarrow B \, = 0 and A→ . C→=0\overrightarrow A \,.\,\overrightarrow C = 0. The vector A→\overrightarrow A is parallel to
View answer and explanation
Correct option: D
B→×C→\overrightarrow B \times \overrightarrow C
Option D (B→×C→\overrightarrow B \times \overrightarrow C) is correct because the cross product of two vectors results in a vector perpendicular to both, and A→\overrightarrow A is perpendicular to both B→\overrightarrow B and C→\overrightarrow C.
23 Medium
23 of 176
Application +4 | -1
A force is inclined at 600{60^0} to the horizontal. If its rectangular component in the horizontal direction is 50 N, then magnitude of the force in the vertical direction is
View answer and explanation
Correct option: C
87 N
For a vector to be a unit vector, the sum of the squares of its components must equal 1. Solving for c gives 0.11\sqrt{0.11}, making option A correct.
24 Medium
24 of 176
Understanding +4 | -1
Minimum number of unequal vectors which can give zero resultant are
View answer and explanation
Correct option: B
three
Option B (three) is correct because at least three unequal vectors are required to achieve a zero resultant, as two unequal vectors cannot cancel each other out.
25 Medium
25 of 176
Understanding +4 | -1
Statement-I: The vector product of a force F⃗\vec{F} and displacement r⃗\vec{r} is equal to the work done.
Statement-II: Work done is not a vector.
View answer and explanation
Correct option: C
Statement-I is false and statement-II is true
Option C is correct because the work done is a scalar quantity, calculated as the dot product of force and displacement, not the vector product.
26 Medium
26 of 176
Understanding +4 | -1
Neglecting the air resistance, the time of flight of a projectile is determined by
View answer and explanation
Correct option: A
Uvertical{U_{\mathrm{vertical}}}
Option A (Uvertical{U_{\mathrm{vertical}}}) is correct because the time of flight depends only on the initial vertical component of velocity and the acceleration due to gravity.
27 Medium
27 of 176
Understanding +4 | -1
Statement-I: The value of i^(j^×k^)+j^(k^×i^)+k^⋅(i^×j^)\hat{\mathrm{i}}(\hat{\mathrm{j}} \times \hat{\mathrm{k}})+\hat{\mathrm{j}}(\hat{\mathrm{k}} \times \hat{\mathrm{i}})+\hat{\mathrm{k}} \cdot(\hat{\mathrm{i}} \times \hat{\mathrm{j}}) is equal to 3
Statement-II: If a^,b^,c^\hat{a}, \hat{b}, \hat{c} are mutually perpendicular unit vectors, then [a^,b^,c^]=1[\hat{a}, \hat{b}, \hat{c}]=1
View answer and explanation
Correct option: A
Statement-I is true and statement-II is true
Statement-I is true because the scalar triple product simplifies to 3. Statement-II is true because the scalar triple product of mutually perpendicular unit vectors is 1.
28 Medium
28 of 176
Analyzing +4 | -1
If the angle between two non-zero vectors A\mathbf{A} and B\mathbf{B} is 120∘120^{\circ}, its resultant CC will be
View answer and explanation
Correct option: C
C>∣A−B∣C>|\mathbf{A}-\mathbf{B}|
Option C (C>∣A−B∣C>|\mathbf{A}-\mathbf{B}|) is correct because when the angle is 120 degrees, the magnitude of the resultant vector is greater than the magnitude of the difference of the two vectors.
29 Medium
29 of 176
Application +4 | -1
A body starts from rest from the origin with an acceleration of 6  m/s26\;m/{s^2} along the x-axis and 8  m/s28\;m/{s^2} along the y-axis. Its distance from the origin after 4 seconds will be
View answer and explanation
Correct option: C
80 m
Option C (80 m) is correct because it accurately calculates the distance from the origin using kinematic equations and the Pythagorean theorem.
30 Medium
30 of 176
Analyzing +4 | -1
Assertion: To cross the river in minimum time, swimmer should swim in a direction perpendicular to the water current.
Reason: In this case river flow helps to cross the river.
View answer and explanation
Correct option: C
If Assertion is True but the Reason is False
Option C is correct because the assertion is true, but the reason is false. Swimming perpendicular minimizes time, but the river flow doesn't *help* cross; it only affects the downstream drift.
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